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N76 [4]
3 years ago
5

Five times the sum of three consecutive integers is 150. what are the integers?

Mathematics
1 answer:
netineya [11]3 years ago
8 0
Alright! Let's start off with the basic from the info given:

150= 5(x+y+z)
First off, since you're looking for x y and z, let's divide both sides by 5:
30= x+y+z

Now let's change y and z written in terms of x:
y= x+1 because it's a consecutive integer
z=x+2 because it's 1 + the value for y

So let's set this up:
30= x + x+1 +x+2

Then simplify
30= 3x + 3

Since you're looking for x, let's subtract 3 then divide by 3
27= 3x
9=x

Now that you have the value of x, plug it into the equations above for y and z:
y=x+1
y= 9+1=10

z= x+2
z= 9+2 =11

Try it out!

(9+10+11) * 5 = 150
(30) * 5 = 150

150 = 150!

So you have x= 9, y= 10, and z=11

Hope this helps!
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Perform the operation and get
Alexandra [31]

Answer:

Step-by-step explanation:

(5-2i) ( 5+2i) = (5^2) - ((2i)^2) = 25 - 4i^2

= 25 - 4(-1) = 25 +4 = 29 + 0i

8 0
3 years ago
A uniform bar of mass $m$ and length $l$ is suspended on a frictionless hinge. A horizontally launched blob of clay of mass $m$
Irina-Kira [14]

Answer:

conservation of angular momentum ; conservation of energy

Step-by-step explanation:

The complete Question is given as follows:

" A uniform bar of mass (m) and length (L) is suspended on a frictionless hinge. A horizontally launched blob of clay of mass (m) strikes the bottom end of the bar and sticks to it. After that, the bar swings upward. What is the minimum initial speed (v) of the blob of clay that would enable the rod to swing a full circle? Which concepts/laws would be most helpful in solving this problem? Select the best answer from the options below.  "

CHOICES

kinematics of rotational motion; conservation of energy

conservation of momentum ; conservation of energy

conservation of angular momentum ; conservation of momentum

conservation of angular momentum ; conservation of energy

conservation of energy ; Newton's laws

Newton's laws ; conservation of angular momentum

conservation of angular momentum ; kinematics of rotational motion

Newton's laws, kinematics of rotational motion

Solution:

- We will apply the conservation of angular momentum M. Note the linear momentum does not remains conserved as the rod stores some energy as the clay sticks to the rod:

                                       M_i = M_f

- Initially the rod was at rest and clay had velocity of v, then M_i can be written as:

                                       M_i = m*v*L

- The final momentum is the combined effect of clay and rod:

                                       M_f = ( m*L^2 + I_rod )*w

- Where w is the angular speed of the rod after impact. And I_rod is the moment of inertia of rod.

                                      I_rod = mL^2 / 3

                                      M_f = ( m*L^2 + m*L^2 /3 )*w = (4*m*L^2 / 3)*w

- Formulate w in terms of initial velocity v:

                                     m*v*L = (4*m*L^2 / 3)*w

                                      0.75*v / L = w

- The minimum amount of velocity required would be enough to complete half of a circle.

- Apply conservation of Energy principle:

                                     T_i + V_i = T_f + V_f

Where, T is the kinetic energy soon after impact and at top most position.

            Assuming, T_f = 0 , for minimum velocity required to complete on circle.

             T_i = 0.5*I_combined*w^2

Where, I_combined = I_clay + I_rod = 4*m*L^2 / 3

And w = 0.75*v / L:

             T_i = 0.5*[4*m*L^2 / 3]*[0.75*v / L]^2

             T_i = 0.5*[m]*[v^2]

Also, V is the potential energy of the clay plus rod system soon after impact and at top most point.

             V_i = 0 ( Datum )

             V_f = V_rod + V_clay

             V_f = m*g*L + m*g*2L = 3*m*g*L

- Plug in the expressions in the energy balance and we get:

                              0.5*[m]*[v^2] + 0 = 0 + 3*m*g*L

                                      v_min = sqrt ( 6*g*L)

- So the choices used were:

conservation of angular momentum ; conservation of energy

                 

             

6 0
3 years ago
A normal population with unknown variance has a mean of 20. Is one likely to obtain a random sample of size 9 from this populati
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Answer:

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3 0
2 years ago
Write the word sentence as an inequality: A number y plus 2 is greater than -5​
MrMuchimi

Answer:

y+2≥5(≥ we don't need the_ because i can't find the symbols)

Step-by-step explanation:

5 0
3 years ago
An amount of $23,000 is borrowed for 11 years at 6.75% interest, compounded annually. If the loan is paid in full at the end of
Pavel [41]

Answer:

Given that,

An amount of $23,000 is borrowed for 11 years at 6.75% interest, compounded annually.

To find the Amount paid back after 11 years.

Explanation:

we know that,

The formula to find the,

Amount after n years of interest rate r% compounded annually is,

A=P(1+\frac{r}{100})^n

where P is the initial amount.

Here, we have that,

P=$23,000

r=6.75

n=11

Substitute the values we get,

A=23000(1+\frac{6.75}{100})^{11}

Solving this we get,

A=23000(1+0.0675)^{11}A=23000(1.0675)^{11}A=23000(2.05138)A=47181.805

Round to the nearest dollar.

A=47181.805\approx47182

Answer is: Amount paid back is $47182 after 11 years

7 0
1 year ago
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